2.1 Molecular Structure
5
2.1.1 Molecular Structure in the Ground State
In most cases, the structural optimization would be performed as to molecule in the
ground state as described in what follows. In general, there could be at least three
kinds of the initial conditions as itemized in the below for starting of the optimization
process:
(1) One can utilize reliable experimental data based on, e.g., the X-ray structural
analysis or its equivalence.
(2) One knows only the shape of the structure in a broad sense without knowing
information on the detailed bond lengths, bond angles, nor dihedral angles.
(3) One should start from molecular formula such as C x H y O z without further
information on the plausible structure.
In any of the above three cases for the optimization process, one ought to actually
start from a certain initial geometry of the target molecule. The initial geometry is
related to a certain point on the PES already shown in Fig. 2.2. Starting from the point
corresponding to the initial molecular geometry, one seeks the energy-minimum point
at which energy of the molecule is the most stable. A more systematic procedure of
this searching for the minimum point on the PES of the ground state as well as of
the excited state is to be described in Sect. 2.1.3. This optimization process and an
estimation of the electronic structure of molecules obtained is now possible in most of
the softwares for theoretical-chemistry calculations employing both the Hartree-Fock
(HF) and the density functional theory (DFT) methods and so on. These methods are
currently most popular in theoretical chemistry to treat the molecular orbitals (MO’s)
of molecules (see Sects. 3.1 and 3.2) with their accompanied electronic structures
and electronic properties of molecules.
Even in case (1), it would be appropriate to find the optimized structure within
the framework of the calculation method employed, since the electronic structure of
the optimized molecular structure by each individual calculation scheme is normally
desirable. It is often useful to start from the structure experimentally obtained (which
is often available by the Crystallographic Information File (CIF) or its equivalence)
as the initial geometry for the optimization process.
Case (2) would be usually encountered in actual optimization process. It is essentially important to start from the plausible initial geometry in order to reduce the
chance of being trapped at inappropriate or undesirable molecular structures as least
as possible by using any available information on the molecule and/or by relying
on one’s chemical intuition with respect to connectivity among atoms included. In
order to build up the initial geometry, one often employs the standard bond lengths
and bond angles, which are normally equipped in each calculation software or listed
in the reference books and so on. There can also appear structural isomers having
less energetically stable structures. Hence care should be taken as to combing out
the structural isomers as exemplified in Fig. 2.3 which give several local minima on
the PES.
Note that it is sometimes better to obtain the initial geometry based on a simpler
calculation routine like the molecular mechanics (MM) method (see Sect. 3.4). This
5
2.1.1 Molecular Structure in the Ground State
In most cases, the structural optimization would be performed as to molecule in the
ground state as described in what follows. In general, there could be at least three
kinds of the initial conditions as itemized in the below for starting of the optimization
process:
(1) One can utilize reliable experimental data based on, e.g., the X-ray structural
analysis or its equivalence.
(2) One knows only the shape of the structure in a broad sense without knowing
information on the detailed bond lengths, bond angles, nor dihedral angles.
(3) One should start from molecular formula such as C x H y O z without further
information on the plausible structure.
In any of the above three cases for the optimization process, one ought to actually
start from a certain initial geometry of the target molecule. The initial geometry is
related to a certain point on the PES already shown in Fig. 2.2. Starting from the point
corresponding to the initial molecular geometry, one seeks the energy-minimum point
at which energy of the molecule is the most stable. A more systematic procedure of
this searching for the minimum point on the PES of the ground state as well as of
the excited state is to be described in Sect. 2.1.3. This optimization process and an
estimation of the electronic structure of molecules obtained is now possible in most of
the softwares for theoretical-chemistry calculations employing both the Hartree-Fock
(HF) and the density functional theory (DFT) methods and so on. These methods are
currently most popular in theoretical chemistry to treat the molecular orbitals (MO’s)
of molecules (see Sects. 3.1 and 3.2) with their accompanied electronic structures
and electronic properties of molecules.
Even in case (1), it would be appropriate to find the optimized structure within
the framework of the calculation method employed, since the electronic structure of
the optimized molecular structure by each individual calculation scheme is normally
desirable. It is often useful to start from the structure experimentally obtained (which
is often available by the Crystallographic Information File (CIF) or its equivalence)
as the initial geometry for the optimization process.
Case (2) would be usually encountered in actual optimization process. It is essentially important to start from the plausible initial geometry in order to reduce the
chance of being trapped at inappropriate or undesirable molecular structures as least
as possible by using any available information on the molecule and/or by relying
on one’s chemical intuition with respect to connectivity among atoms included. In
order to build up the initial geometry, one often employs the standard bond lengths
and bond angles, which are normally equipped in each calculation software or listed
in the reference books and so on. There can also appear structural isomers having
less energetically stable structures. Hence care should be taken as to combing out
the structural isomers as exemplified in Fig. 2.3 which give several local minima on
the PES.
Note that it is sometimes better to obtain the initial geometry based on a simpler
calculation routine like the molecular mechanics (MM) method (see Sect. 3.4). This